I don’t think the realm of forms is directly accessible to us. It’s not a place where perception is possible. Unchanging, eternal, infinite.
But I think understanding – what is called in the East, realisation – is always possible, and Plato’s works are directed towards comprehension. Sometimes it appears that the physical world is unimportant. Grasp the underlying reality, and the imperfect perception around us is tawdry and flawed.
Plato could not have written much of what he did without understanding, himself. There’s a passage in the Meno where geometry is used to illustrate a concept. The pure and perfect understanding of mathematics and geometry is one way of approaching the realm of forms.
Extend that to some of the more abstract topics he covered – Love, Justice, the nature of humanity – and it seems clear to me that Plato knew of what he was talking.
Another way of looking at it is that flash of insight we get now and then. More than a gut feeling, we sometimes instinctively know something is right. It resonates. It is a lightbulb moment. You know what I mean?
That sort of experience is where we are close to the realm of forms which underlies this temporary cosmos we inhabit.
In my own ignorant opinion, that is.